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An evaluation of oceanic containment strategies for anthropogenic carbon dioxide is presented. Energy conservation is also addressed through an input hydrocarbon-fuel consumption function. The effectiveness of the proposed countermeasures is determined from atmospheric CO2 concentration predictions. A previous box model with a diffusive deep ocean is adapted and applied to the concept of fractional CO2 injection in 500 m deep waters. Next, the contributions of oceanic calcium carbonate sediment dissolution, and of deep seawater renewal, are included. Numerical results show that for CO2 direct removal measures to be effective, large fractions of anthropogenic carbon dioxide have to be processed. This point favors fuel pre-processing concepts. The global model also indicates that energy conservation, i. e. a hydrocarbon-fuel consumption slowdown, remains the most effective way to mitigate the greenhouse effect, because it offers mankind a substantial time delay to implement new energy production alternatives.